类Helmholtz方程的无网格局部Petrov-Galerkin法

将无网格局部Petrov-Galerk in方法和改进的移动最小二乘近似相结合,求解了二维类Helmholtz方程。改进的移动最小二乘近似采用加权正交函数系作为基函数,与传统的移动最小二乘近似相比,改进的移动最小二乘近似中的系数矩阵变成了非奇异的对角矩阵,因而无需计算系数矩阵的逆。数值结果表明该方法数值精度高,收敛速度快。

The meshless local Petrov-Galerkin method for solving the analogic Helmholtz equation

In this paper,the meshless local Petrov-Galerkin method with improved moving least-squares approximation for two-dimensional analogic Helmholtz equation is discussed.In the improved moving least-squares approximation,an orthogonal function system with a weight function is used as the basis function.In comparison with the existing moving least-squares approximation,the system matrix in the improved moving least-squares approximation is a nonsingular diagonal matrix and can be solved without obtaining the inverse matrix.In numerical examples,the convergence and stability of the presented method are studied and accurate results are obtained.